They (or the company that buys them) should license BB10 to others. Like Microsoft does with windows mobile... It's the only path I can see for the blackberry OS to survive. Otherwise they'll be utterly crushed.
The problem is Blackberry is a hardware manufacturer, so they'd need a huge volume of sales in software to make up what they would lose in hardware.
That said, BB10 doesn't really offer anything compelling above Android for manufactures, and additional hardware isn't going to massively change their market share. BB customers have never been driven by cutting edge phones. Their application marketplace is so bad that there's no reason for general consumers to want to buy into the platform.
They definitely wouldn't survive a transition to a software company.
The reason their customers buy them has nothing to do with the hardware and everything to do with BBM. The only way out for them is as a service provider on alternate (Android, Windows, iOS) platforms.
Going private may enable them to continue to do this; any purchaser that makes sense (Microsoft) would be buying their customer list and the BBM brand. Dell buying them would be a Palm goes to HP level farce.